Customized Analytic Center Cutting Plane Methods for the Discrete-Time Integral Quadratic Constraint Problem. Issue 25 (2022) - Jaoude, Dany Abou; Farhood, Mazen
Abstract: This paper deals with the design of efficient algorithms for solving analysis problems formulated in the integral quadratic constraint (IQC) framework. The oracle for the discrete-time IQC problem is coupled with the analytic center cutting plane method (ACCPM), and the implementation of the ACCPM is customized to leverage promising features of the oracle such as the possibility of generating strictly separating hyper planes between the candidate solution and feasible set and the possibility of generating more than one separating hyper plane. Such customizations may be needed if the ACCPM is to be used as part of recursive IQC synthesis algorithms for practical problems. Numerical examples are generated to compare various versions of the ACCPM, namely, with single center cuts, single deep cuts, and two center cuts.